To understand where the sound is concentrated after reflecting off the back wall of the depression in the temple, we can use some principles of geometry and acoustics. The spherical shape of the depression plays a crucial role in how sound waves behave when they encounter surfaces. Let's break this down step by step.
The Geometry of the Situation
The depression in the wall is described as having a spherical shape with a radius of 2.50 meters. This means that if you were to visualize it, the deepest point of the depression is at the center of this sphere. The worshiper stands 2.00 meters away from this deepest point, along the center line of the depression.
Understanding Sound Reflection
When the worshiper whispers, the sound waves emanate from their mouth in all directions. However, because of the spherical shape of the depression, these sound waves will reflect off the curved surface of the wall. The key principle here is that sound waves reflect off surfaces in a manner similar to light, following the law of reflection: the angle of incidence equals the angle of reflection.
Finding the Focus Point
In a spherical depression, sound waves that hit the wall will converge at a specific point after reflection. This point is known as the focus of the sphere. For a sphere, the focus lies along the axis of symmetry of the sphere. Given that the radius of the sphere is 2.50 meters, the focus will be located at the center of the sphere, which is 2.50 meters from the deepest point of the depression.
- Deepest point of the depression: 0 m
- Radius of the sphere: 2.50 m
- Focus of the sphere: 2.50 m from the deepest point
- Worshiper's position: 2.00 m from the deepest point
Since the worshiper is standing 2.00 meters away from the deepest point, the sound waves will reflect off the back wall and converge at the focus, which is 2.50 meters from the deepest point. This means that the sound will be concentrated at a point that is 0.50 meters behind the worshiper, along the center line of the depression.
Conclusion
In summary, after the worshiper whispers, the sound waves will reflect off the back wall of the spherical depression and concentrate at a point that is 0.50 meters behind the worshiper. This phenomenon illustrates how the shape of a space can significantly influence sound behavior, creating a unique acoustic environment in the temple.
